Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.2 Definition of Vector Spaces - Problems - Page 262: 17

Answer

See below

Work Step by Step

General form of vector space $V$ is $A=\begin{bmatrix} a_{11} & a_{12} & .. & a_{1n} \\ a_{21} & a_{22} & ... & a_{2n} \\ . & . & ... & . \\ a_{m1} & a_{m2} & ... & a_{mn} \end{bmatrix}$ with $a_{ij} \in R$ we can see that zero vector in $V$ is $\begin{bmatrix} 0 & 0 & ... & 0 \\ 0 & 0 & ... & 0 \\ . & . & ... & . \\ 0 & 0 & ... & 0 \end{bmatrix}$ Hence, additive inverse $-A=\begin{bmatrix} -a_{11} & -a_{12} & .. & -a_{1n} \\ -a_{21} & -a_{22} & ... & -a_{2n} \\ . & . & ... & . \\ -a_{m1} & -a_{m2} & ... & -a_{mn} \end{bmatrix}$
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